Does the heat-trapping effect of CO2 have any effect on the temperature of the planet?
Let’s do the numbers. . .
Let’s take, for the sake of argument, the volume of Earth’s atmosphere. Let’s just deal with the lowest kilometer of the atmosphere. Above that, temps drop, typically at a rate of about 1°C every 200M on average, and heat above that isn’t directly contributing to heating the water in the ocean. So the surface area of the Earth is 510,072,000 km^2 which is 510,072,000 km^3 since we’re just using the bottom km. Now, I know that 30% of that is not in contact with the water and therefore not contributing to heating any water, but it’s all a giant heat sink, and the more air, the better for your argument.
And let’s take, for example the volume of the top 10 meters of water on the ocean. The oceans are about 361.9*e^6 square kilometers, top ten meters, divide by 100 gives us 3,619,000 cubic kilometers of water.
So the question is, how many degrees of heat does that air have to give up to heat that top 10 meters of water by 1°C?
Well, first we have to figure out how much mass our water and air is. Water is by definition 1000Kg per cubic meter, and there are 1*e^9 cubic meters in a cubic km. This gives us 1*e^15 grams of water per cubic km. Multiply that by our volume, and we have 3.619*e^21 grams of water. Yeah, yeah, salinity, temperature, etc. . . On the scale we’re working at they’re negligible to the final result, as you shall see.
For the air, we have 1.2041 kg per cubic meter at sea level, times 1*e^9 cubic meters in a cubic km, times 1000 grams in a kg, times 510,072,000 km^3 on the planet, gives us 614.1776952*e^18 grams of air.
The heat capacity of water is 4.184 joules per gram. For you freshmen that means you have to add 4.184 joules to a gram of water to heat it by 1°C. The formula is Q= mc∆T where Q is the energy, m is the mass, c is the heat capacity and ∆T is the change of temperature. That means to raise the temperature of the top 10 meters of the ocean by 1°C, you need to add 1.5141896E+22 joules of energy.
Now the ocean heats up by direct exposure to the sun, which amounts to a HUGE input of energy. But that’s not what we’re talking about. The premise is that the CO2 in the atmosphere is trapping solar energy and that trapped heat is warming the oceans. Essentially the CO2 is supposedly contributing to heating the air, which then heats the oceans. So how much hotter does the air have to get through CO2 warming to cause a 1°C rise in ocean temperatures as a result?
To frame this, we have a known energy amount, 1.5141896E+22 joules, a known mass of air, 614.1776952*e^18g and a heat capacity of 1.01 joules per gram. Rearranging our formula to solve for temperature, Q/mc= ∆T, gives us 24°C.
So your CO2 heat contribution would have to raise the atmosphere by 24°C, all of which would then have to be transferred to the water to raise the top 10 meters by 1°C. It would actually have to raise it much higher, because this assumes a 100% efficient heat transfer, which is wildly optimistic.
I gave a lot of leeway in this model. The actual part of the atmosphere that needs to be heated is much smaller, requiring far higher temps to get the same effect. Ocean mixing will take some of the heat to the depths, resulting in effectively much larger volumes of water to be heated than we postulated. Now, are you going to tell me with a straight face that CO2 greenhouse effect contributes enough thermal energy to the atmosphere to cause a significant or even measurable change in ocean temperatures? If you still hold to this, then you’re a special kind of stupid.
Global warming is that the planet's ecosystem is heating up. This is the atmosphere AND the ocean, since the ocean actually controls the atmospheric temperature. Posit any mechanism you like, if you don't affect the ocean temperature, you don't affect the climate.
CO2 doesn't absorb, it re-radiates, trapping the heat and not reflecting it back to space. The point is, how many joules of solar radiation are received by the sun, and how many are reflected back into space? That which is not reflected is absorbed, on a system scale. CO2 prevents reflection back into space, therefore the system (i.e. primarily the atmosphere and secondarily the ocean) must absorb it.
It's a cumulative effect, and my point was to demonstrate that the mechanism by which the atmospheric temperature heats the ocean is of no consequence.
Do the math backwards: How much does the ocean have to heat to heat the atmosphere by 1°C? The ratios are the same: 1/24th of a degree. The ocean is exceedingly efficient at controlling the temperature of the atmosphere. It can cause dramatic changes of atmospheric temperature without changing it's own temperature hardly at all. Anyone living close to the sea knows this. This is what drives hurricanes and typhoons. This is why Northern Europe is a fertile agricultural area instead of a sub-arctic tundra.
The single biggest factor in heat absorption by the climate system is by direct solar heating of the ocean. The ocean is a giant heat sink which dramatically affects the temperature of the air above it. As the air heats up, more water vapor is absorbed into the atmosphere, which convects up and condenses to clouds. The clouds increase the surface albedo of the planet, reducing the amount of sunlight that hits the ocean to warm it, cooling the ocean. It's a feedback loop, and the most important one in terms of regulating the climate and distributing heat around the planet. Water vapor is a greenhouse gas and is responsible for 95% of the greenhouse effect, and the amount of water vapor is highly variable based on ocean heating. compared to this giant heat feedback mechanism, the contribution of CO2 is negligible.
In fact there's no evidence to say that CO2 is even a leading factor in climate fluctuations or a trailing one.
Climate changes. It always has. The change in solar irradiance since the Little Ice Age is 3 W/m2. The change in forcing due to CO2 is 1.5 W/m2 per doubling and since we've only had 0.43 doublings since the Little Ice Age. That means CO2 rise since the Little Ice Age has added .43 x 1.5 = 0.65 watts compared to 3 watts for the sun. That's a 5-fold difference. What is primarily driving climate warming, the sun or CO2?
Let’s do the numbers. . .
Let’s take, for the sake of argument, the volume of Earth’s atmosphere. Let’s just deal with the lowest kilometer of the atmosphere. Above that, temps drop, typically at a rate of about 1°C every 200M on average, and heat above that isn’t directly contributing to heating the water in the ocean. So the surface area of the Earth is 510,072,000 km^2 which is 510,072,000 km^3 since we’re just using the bottom km. Now, I know that 30% of that is not in contact with the water and therefore not contributing to heating any water, but it’s all a giant heat sink, and the more air, the better for your argument.
And let’s take, for example the volume of the top 10 meters of water on the ocean. The oceans are about 361.9*e^6 square kilometers, top ten meters, divide by 100 gives us 3,619,000 cubic kilometers of water.
So the question is, how many degrees of heat does that air have to give up to heat that top 10 meters of water by 1°C?
Well, first we have to figure out how much mass our water and air is. Water is by definition 1000Kg per cubic meter, and there are 1*e^9 cubic meters in a cubic km. This gives us 1*e^15 grams of water per cubic km. Multiply that by our volume, and we have 3.619*e^21 grams of water. Yeah, yeah, salinity, temperature, etc. . . On the scale we’re working at they’re negligible to the final result, as you shall see.
For the air, we have 1.2041 kg per cubic meter at sea level, times 1*e^9 cubic meters in a cubic km, times 1000 grams in a kg, times 510,072,000 km^3 on the planet, gives us 614.1776952*e^18 grams of air.
The heat capacity of water is 4.184 joules per gram. For you freshmen that means you have to add 4.184 joules to a gram of water to heat it by 1°C. The formula is Q= mc∆T where Q is the energy, m is the mass, c is the heat capacity and ∆T is the change of temperature. That means to raise the temperature of the top 10 meters of the ocean by 1°C, you need to add 1.5141896E+22 joules of energy.
Now the ocean heats up by direct exposure to the sun, which amounts to a HUGE input of energy. But that’s not what we’re talking about. The premise is that the CO2 in the atmosphere is trapping solar energy and that trapped heat is warming the oceans. Essentially the CO2 is supposedly contributing to heating the air, which then heats the oceans. So how much hotter does the air have to get through CO2 warming to cause a 1°C rise in ocean temperatures as a result?
To frame this, we have a known energy amount, 1.5141896E+22 joules, a known mass of air, 614.1776952*e^18g and a heat capacity of 1.01 joules per gram. Rearranging our formula to solve for temperature, Q/mc= ∆T, gives us 24°C.
So your CO2 heat contribution would have to raise the atmosphere by 24°C, all of which would then have to be transferred to the water to raise the top 10 meters by 1°C. It would actually have to raise it much higher, because this assumes a 100% efficient heat transfer, which is wildly optimistic.
I gave a lot of leeway in this model. The actual part of the atmosphere that needs to be heated is much smaller, requiring far higher temps to get the same effect. Ocean mixing will take some of the heat to the depths, resulting in effectively much larger volumes of water to be heated than we postulated. Now, are you going to tell me with a straight face that CO2 greenhouse effect contributes enough thermal energy to the atmosphere to cause a significant or even measurable change in ocean temperatures? If you still hold to this, then you’re a special kind of stupid.
Global warming is that the planet's ecosystem is heating up. This is the atmosphere AND the ocean, since the ocean actually controls the atmospheric temperature. Posit any mechanism you like, if you don't affect the ocean temperature, you don't affect the climate.
CO2 doesn't absorb, it re-radiates, trapping the heat and not reflecting it back to space. The point is, how many joules of solar radiation are received by the sun, and how many are reflected back into space? That which is not reflected is absorbed, on a system scale. CO2 prevents reflection back into space, therefore the system (i.e. primarily the atmosphere and secondarily the ocean) must absorb it.
It's a cumulative effect, and my point was to demonstrate that the mechanism by which the atmospheric temperature heats the ocean is of no consequence.
Do the math backwards: How much does the ocean have to heat to heat the atmosphere by 1°C? The ratios are the same: 1/24th of a degree. The ocean is exceedingly efficient at controlling the temperature of the atmosphere. It can cause dramatic changes of atmospheric temperature without changing it's own temperature hardly at all. Anyone living close to the sea knows this. This is what drives hurricanes and typhoons. This is why Northern Europe is a fertile agricultural area instead of a sub-arctic tundra.
The single biggest factor in heat absorption by the climate system is by direct solar heating of the ocean. The ocean is a giant heat sink which dramatically affects the temperature of the air above it. As the air heats up, more water vapor is absorbed into the atmosphere, which convects up and condenses to clouds. The clouds increase the surface albedo of the planet, reducing the amount of sunlight that hits the ocean to warm it, cooling the ocean. It's a feedback loop, and the most important one in terms of regulating the climate and distributing heat around the planet. Water vapor is a greenhouse gas and is responsible for 95% of the greenhouse effect, and the amount of water vapor is highly variable based on ocean heating. compared to this giant heat feedback mechanism, the contribution of CO2 is negligible.
In fact there's no evidence to say that CO2 is even a leading factor in climate fluctuations or a trailing one.
Climate changes. It always has. The change in solar irradiance since the Little Ice Age is 3 W/m2. The change in forcing due to CO2 is 1.5 W/m2 per doubling and since we've only had 0.43 doublings since the Little Ice Age. That means CO2 rise since the Little Ice Age has added .43 x 1.5 = 0.65 watts compared to 3 watts for the sun. That's a 5-fold difference. What is primarily driving climate warming, the sun or CO2?
I have read your sketch of numbers on your blog and have to point out one thing: First of all, you are considering your whole model as a static system. As you even point out in your blog post, these effects are cumulative, so I'm surprised that even saying that you used a static model. Secondly, the water cycle, which feeds to and from the ocean, interacts with more of the surface of the earth than just the surface of the ocean. Third, and I believe most damningly to your argument, the atmosphere doesn't have to heat up in order to transmit thermal energy to the ocean (The ocean can absorb reflected IR directly)
ReplyDelete1) Yes, for the purpose of this discussion, I am considering the model as a static system. The point is to show that water temperature drives air temperature far more than vice versa. A static system is a worst case scenario, as any of the dynamic factors primarily remove heat from the water, making my argument even stronger.
Delete2) Yes, as I pointed out that works in favor of the argument that the air temperature heats the water.
3) Not damning at all. The atmosphere does transmit the bulk of the Sun's heating energy to the ocean without heating up. This is exactly the point. The Anthropogenic Global Warming caim is that the additional CO2 in the atmosphere is causing the ocean to warm. This CO2 is not a passive conduit of heat, the mechanism is supposedly that the CO2 absorbs the radiated heat from the surface of the Earth in its absorption spectrum (14.5 -15.5µm wavelength), which heats up the atmosphere, which in turn heats up the ocean. The point of this discussion is that any such heating is negligible compared to the normal heating of the ocean by direct sunlight. There's simply not enough air - which has a small heat capacity - and far too much water - which has a large heat capacity - for any sort of significant heat transfer from the air to the oceans.